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Semicircles are constructed on AB, AC, and BC.  A circle is tangent to all three semicircles.  Find the radius of the circle.

 

 Mar 31, 2024
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The radius of the circle is r.

\((r+1)^2=(2-r)^2+1^2\\r^2+2r+1=4-4r+r^2+1\\ 6r=4\\ \color{blue}r=\dfrac{2}{3}\)

laugh !

 Mar 31, 2024

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